I plan to run the Bitcoin client on an underutilized server at an off-site location. I cannot remote into it and won't be back to that location for at least a couple of months from now. Thus I won't know if it generated any Bitcoin, nor would I be able to transfer it before my next visit.

Should any Bitcoin be generated for it, will the address that the Bitcoin is sent to be the address that was initially generated for the client?

I plan to run the Bitcoin client on an underutilized server at an off-site location. I cannot remote into it and won't be back to that location for at least a couple of months from now. Thus I won't know if it generated any Bitcoin, nor would I be able to transfer it before my next visit.

Should any Bitcoin be generated for it, will the address that the Bitcoin is sent to be the address that was initially generated for the client?

Additionally, if I created a backup of the wallet and have it with me, I should be able to fire up another client here, restore the wallet and be able to transfer the Bitcoin away, correct?

no, each block generation bounty gets credited to a new address, so monitoring the 'first address' will not be of use.

the bitcoin client now pre-generates a 'pool' of keys, sized 100 by default. i /think/ (but am not sure) that the addresses used for generation are also taken from this pool. if that is the case, then if you make a backup of the wallet and look at it on your local machine periodically, you'll be able to see the generation credits in your wallet backup (at least until you run out of the 100 pool addresses - depending on how fast your remote machine is generating, it may happen very fast or quite slowly).

but since i'm not sure if the pool addresses are used for generation, you should get confirmation on that from someone who knows what's up.

Also, I think there may be some cases where a keypool address would be thrown away without a generation (like if Bitcoin crashes, or maybe even when it shuts down).

The keypool IS used for coin-generation transactions.

And the way it is implemented, it should never throw away keys. If I recall correctly, there is a very small chance if you lose power or bitcoin crashes a key from the keypool could be used twice. But that has no bad effects, it is just very unusual.

How often do you get the chance to work on a potentially world-changing project?